Extensions of Rings of Holomorphic Functions.
Extremal Kähler metrics on blow-ups of parabolic ruled surfaces
New examples of extremal Kähler metrics are given on blow-ups of parabolic ruled surfaces. The method used is based on the gluing construction of Arezzo, Pacard and Singer [5]. This enables to endow ruled surfaces of the form with special parabolic structures such that the associated iterated blow-up admits an extremal metric of non-constant scalar curvature.
Extremal metrics and lower bound of the modified K-energy
We provide a new proof of a result of X.X. Chen and G.Tian [5]: for a polarized extremal Kähler manifold, the minimum of the modified K-energy is attained at an extremal metric. The proof uses an idea of C. Li [16] adapted to the extremal metrics using some weighted balanced metrics.
Extremal plurisubharmonic functions
We study different notions of extremal plurisubharmonic functions.
Extremal plurisubharmonic functions and invariant pseudodistances
Extremal plurisubharmonic functions in
Extremal plurisubharmonic functions of linear growth on algebraic varieties.
Extreme plurisubharmonic singularities
A plurisubharmonic singularity is extreme if it cannot be represented as the sum of non-homothetic singularities. A complete characterization of such singularities is given for the case of homogeneous singularities (in particular, those determined by generic holomorphic mappings) in terms of decomposability of certain convex sets in ℝⁿ. Another class of extreme singularities is presented by means of a notion of relative type.
Factoriality of a ring of holomorphic functions
Factorization of functions in weighted Bergman spaces
Factorization of rank two theta functions. II. Proof of the Verlinde formula.
Factorization of semisimple discrete representations of Kähler groups.
Factorization of uniformly holomorphic functions
Let E be a complex Hausdorff locally convex space such that the strong dual E’ of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states that the...
Faisceaux analytiques semi-cohérents
Nous définissons deux notions nouvelles en géométrie analytique réelle, celle de fonction Nash-analytique et celle de faisceau semi-cohérent. Avec ces notions, nous obtenons des théorèmes de cohérence analogues à ceux du cas complexe (théorème de cohérence d’Oka, théorème de l’image directe, cohérence d’un ensemble analytique complexe).
Faisceaux constructibles quasi-unipotents
Faisceaux pervers dont le support singulier est une courbe plane
Familias compactas de funciones holomorfas con desarrollo asintótico en abierto de Cn.
Let U be an open convex subset of Cn, n belonging to N, such that the set of all polinomies is dense in the space of all holomorphic and complex functions on U, (H(U), t0), where t0 is the open-compact topology.We endow the space HK(U) of all holomorphic functions on U that have asymptotic expansion at the origin with a metric and we study a particular compact subset of HK(U).
Familien komplexer Räume mit streng pseudokonvexer spezieller Faser
Families of analytic discs in with boundaries on a prescribed submanifold
Families of Curves on Surfaces.